How would I simplify (3 sqrt -5 + 2)(4 sqrt -12 – 1)?
I think that I would have to use the distributive property, but does anyone know the steps to solve this problem?
NO
How could you possibly equate all those square roots and imaginary numbers to 18?
Although I do see I made a typo. I missed the -5.
(3√-5 + 2)(4√-12 - 1)
(3√-5 + 2)(8√-3 - 1)
(3√-5)(8√-3) + (3√-5)(-1) + (2)(8√-3) + (2)(-1)
24√15 - 3√-5 + 16√-3 - 2
so why do you think the answer is 18?
umm, yes - use the distributive property.
(3√5 + 2)(4√-12 - 1)
(3√5 + 2)(8√-3 - 1)
(3√5)(8√-3) + (3√5)(-1) + (2)(8√-3) + (2)(-1)
24√-15 - 3√5 + 16√-3 - 2
Thank you! Would the end answer be 18?
To simplify the expression (3√-5 + 2)(4√-12 - 1), you are correct that you need to use the distributive property. Here are the steps to solve this problem:
Step 1: Apply the distributive property by multiplying the first term (3√-5) with each term inside the second parentheses (4√-12 - 1), and then multiply the second term (2) with each term inside the second parentheses:
(3√-5 + 2)(4√-12 - 1) =
(3√-5 * 4√-12) + (3√-5 * -1) + (2 * 4√-12) + (2 * -1)
Step 2: Simplify each of the four terms obtained in the previous step. To do this, you need to simplify the square roots and multiply the coefficients:
Term 1: (3√-5 * 4√-12) = 12√(-5)(-12) = 12 * √60 = 12√(2 * 2 * 3 * 5) = 12 * 2√(3) = 24√(3)
Term 2: (3√-5 * -1) = -3√-5
Term 3: (2 * 4√-12) = 8√(-12) = 8√(-1 * 3 * 4) = 8 * 2i√(3) = 16i√(3)
Term 4: (2 * -1) = -2
Step 3: Combine the simplified terms obtained in Step 2:
24√(3) - 3√-5 + 16i√(3) - 2
This is the simplified form of the expression (3√-5 + 2)(4√-12 - 1).